Compressed sensing with sparse frame representations is seen to have much greater range of practical applications than that orthonormal bases. In such settings, one approach recover the signal known as ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -analysis. We expand in this paper performance analysis by providing a weaker recovery condition existing results literature. Our also broadly based on general frames and alter native dual...

Abstract The intensification of Northern Hemisphere Glaciation (iNHG) with the onset glacial‐interglacial cycles at ∼2.7 Ma had a profound impact on global climate system. However, there have been few systemic assessments response orbital‐scale East Asian summer monsoon (EASM) variability to iNHG, partly due controversies regarding interpretation dominant orbital rhythms EASM. Here, we present grain size and other proxy records from mainly silt‐sized lacustrine‐fluvial deposits in northern...

This article studies the problem of reconstructing spectrally sparse signals from a small random subset time domain samples via low-rank Hankel matrix completion with aid prior information. By leveraging structure in lifting and similarity between their information, we propose convex method to recover undersampled signals. The proposed approach integrates inner product desired signal its information lift into vanilla completion, which maximizes correlation Theoretical analysis indicates that...

We provide another framework of iterative algorithms based on thresholding, feedback and null space tuning for sparse signal recovery arising in representations compressed sensing. Several thresholding with various feedbacks are derived. Convergence results also provided. The core algorithm is shown to converge finitely many steps under a (preconditioned) restricted isometry condition. seen as exceedingly effective fast, particularly large scale problems. Numerical studies about the...

Localizing a cloud of points from noisy measurements subset pairwise distances has applications in various areas, such as sensor network localization and reconstruction protein conformations nuclear magnetic resonance measurements. Drineas et al. proposed natural two-stage approach, named singular value decomposition (SVD)-multidimensional scaling (MDS), for this purpose at the 2006 3rd Annual IEEE Communications Society on Sensor Ad Hoc Networks. This approach consists low-rank matrix...

The spindle box is responsible for power transmission, supporting the rotating parts and ensuring rotary accuracy of workpiece in heavy-duty machine tool. Its assembly quality crucial to ensure reliable supply stable operation tool process large load cutting force. Therefore, accurate diagnosis faults great significance improving efficiency outgoing quality. In this paper, common fault types characteristics heavy horizontal lathe are analyzed first, original vibration signals various...

This paper studies the problem of accurately recovering a structured signal from small number corrupted sub-Gaussian measurements. We consider three different procedures to reconstruct and corruption when kinds prior knowledge are available. In each case, we provide conditions (in terms measurements) for stable recovery with added unstructured noise. Our results theoretically demonstrate how choose regularization parameters in both partially fully penalized shed some light on relationships...

This paper considers the problem of recovering a structured signal from relatively small number noisy measurements with aid similar which is known beforehand. We propose new approach to integrate prior information into standard recovery procedure by maximizing correlation between knowledge and desired signal. then establish performance guarantees (in terms measurements) for proposed method under sub-Gaussian measurements. Specific signals including sparse vectors, block-sparse low-rank...

Signals with sparse representations in frames comprise a much more realistic model of nature, it is therefore highly desirable to extend the compressed sensing methodology redundant dictionaries (or frames) as opposed orthonormal bases only. In generalized setting, standard approach recover signal known ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -synthesis Basis Pursuit). this paper, we present performance analysis which...

This paper studies the problem of accurately recovering a structured signal from small number corrupted sub-Gaussian measurements. We consider three different procedures to reconstruct and corruption when kinds prior knowledge are available. In each case, we provide conditions for stable recovery with added unstructured noise. The key ingredient in our analysis is an extended matrix deviation inequality isotropic matrices.

In [1], a sharp phase transition has been numerically observed when constrained convex procedure is used to solve the corrupted sensing problem. this paper, we present theoretical analysis for phenomenon. Specifically, establish threshold below which fails recover signal and corruption with high probability. Together work in prove that occurs around sum of squares spherical Gaussian widths two tangent cones. Numerical experiments are provided demonstrate correctness sharpness our results.

Abstract Long-range entanglement is an important aspect of the topological orders, so efficient methods to characterize long-range are often needed. In this regard, entropy (TEE) used for such a purpose but experimental observation TEE in order remains challenge. Here, we propose scheme observe by constructing specific minimum states (MESs). We then experimentally construct classical microwave analogs MESs and simulate nontrivial with Kitaev toric code, which agreement theoretical...

Compressed sensing (CS) with prior information concerns the problem of reconstructing a sparse signal aid similar which is known beforehand. We consider new approach to integrate into CS via maximizing correlation between knowledge and desired signal. then present geometric analysis for proposed method under sub-Gaussian measurements. Our results reveal that if good enough, can improve performance standard CS. Simulations are provided verify our results.

This paper studies the problem of recovering a structured signal from relatively small number corrupted non-linear measurements. Assuming that and corruption are contained in some structure-promoted set, we suggest an extended Lasso to disentangle corruption. We also provide conditions under which this recovery procedure can successfully reconstruct both

Corrupted sensing concerns the problem of recovering a high-dimensional structured signal from collection measurements that are contaminated by unknown corruption and unstructured noise.In case linear measurements, recovery performance different convex programming procedures (e.g., generalized Lasso its variants) is well established in literature.However, practical applications digital processing, quantization process inevitable, which often leads to non-linear measurements.This paper...

In order to ensure safely and effective operation of the transmission line, condition monitoring lines is widely applied discover dangerous points monitor surrounding weather conditions. Since run across fields, adopting mobile communication network carry out data very convenience. The cost directly proportional whose flow for transmission. reduce cost, compressed sensing technology image compression reconstruction in this paper. proposed method uses sparse random matrix sample images on...

The stochastic gradient matching pursuit algorithm requires the sparsity of signal as prior information. However, this information is unknown in practical applications, which restricts applications to some extent. An improved method was proposed overcome problem. First, a pre-evaluation strategy used evaluate and estimated initial sparsity. Second, if number columns candidate atomic matrix smaller than that rows, least square solution calculated, otherwise, set zero. Finally, current...

Covariance matrix estimation concerns the problem of estimating covariance from a collection samples, which is extreme importance in many applications. Classical results have shown that $O(n)$ samples are sufficient to accurately estimate $n$-dimensional independent Gaussian samples. However, practical applications, received signal might be correlated, makes classical analysis inapplicable. In this paper, we develop non-asymptotic for correlated Our theoretical show error bounds determined...